[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:05.48,Default,,0000,0000,0000,,Now let me shift the frequency a little\Nbit, just to see what it looks like. So to
Dialogue: 0,0:00:05.48,0:00:10.63,Default,,0000,0000,0000,,shift that center frequency. In other\Nwords, off zero because we haven't done
Dialogue: 0,0:00:10.63,0:00:24.38,Default,,0000,0000,0000,,anything off zero yet. We'll just go over\Nhere, and say, ten. Alright, now you may
Dialogue: 0,0:00:24.38,0:00:29.87,Default,,0000,0000,0000,,go like, what happened? Alright? Well I'll\Ntell you what happened. Moment here, this
Dialogue: 0,0:00:29.87,0:00:35.22,Default,,0000,0000,0000,,goes up. So first of all, I just shifted\Nthe center frequency over by ten, still
Dialogue: 0,0:00:35.22,0:00:40.84,Default,,0000,0000,0000,,fixed in frequency. Now the top picture is\Ninteresting. Now I am looking at this, my
Dialogue: 0,0:00:40.84,0:00:45.71,Default,,0000,0000,0000,,center frequency is zero and zero\Nfrequency, what does that mean? Cosine
Dialogue: 0,0:00:45.71,0:00:50.20,Default,,0000,0000,0000,,zero X, n oscillations. Now my center\Nfrequency is cosine ten X, well cosine ten
Dialogue: 0,0:00:49.95,0:00:54.84,Default,,0000,0000,0000,,X. I mean I have this, I have this e to\Nthe I ten X multiplying everything. So you
Dialogue: 0,0:00:54.84,0:00:59.54,Default,,0000,0000,0000,,see this here? Looks like a cosine 10x\Nsitting on that thing. So I have a bump,
Dialogue: 0,0:00:59.54,0:01:04.30,Default,,0000,0000,0000,,this hyperbolic secant times the cosine\Nten X. So it's a wave packet, oscillation.
Dialogue: 0,0:01:04.30,0:01:09.01,Default,,0000,0000,0000,,So if you want to get rid of it, you'd\Nsay, well how about if I just look at the
Dialogue: 0,0:01:09.01,0:01:20.62,Default,,0000,0000,0000,,absolute value of that thing? And if you\Ndo that, it takes away the phase, and it
Dialogue: 0,0:01:20.62,0:01:25.58,Default,,0000,0000,0000,,gives you back that. Okay, all that\Noscillation was, was having a group of
Dialogue: 0,0:01:25.58,0:01:30.27,Default,,0000,0000,0000,,carrier frequencies sitting around in\Nthere. It's a frequency component and it
Dialogue: 0,0:01:30.27,0:01:34.89,Default,,0000,0000,0000,,has a phase. You just get rid of them.\NAbsolute value, stuff like that. It's all
Dialogue: 0,0:01:34.89,0:01:39.88,Default,,0000,0000,0000,,I care about. You may care about the phase\Nfor more important reasons later, but for
Dialogue: 0,0:01:39.88,0:01:44.68,Default,,0000,0000,0000,,right now, it's all we care about. Notice\Na couple things, if I had a lot of noise
Dialogue: 0,0:01:44.68,0:01:52.24,Default,,0000,0000,0000,,on here. I'm going to bury all of this so\Nin fact let's, let's, let's bury all of it
Dialogue: 0,0:01:52.24,0:01:56.82,Default,,0000,0000,0000,,and just put it in a sea of noise and your\Ngoing to see that. Basically, if I take
Dialogue: 0,0:01:56.82,0:02:01.68,Default,,0000,0000,0000,,all of this out and this is all noisy then\Nwhat do I do. Okay, first thing you gotta
Dialogue: 0,0:02:01.68,0:02:06.24,Default,,0000,0000,0000,,do, if you have this all buried in noise,\Nfigure out where is this, where's that
Dialogue: 0,0:02:06.24,0:02:10.97,Default,,0000,0000,0000,,center frequency. Second thing you do is,\Nonce you know where the center frequency
Dialogue: 0,0:02:10.97,0:02:15.47,Default,,0000,0000,0000,,is, you can build the filter there, and\Nbuild the filter so you can go back to
Dialogue: 0,0:02:15.47,0:02:23.06,Default,,0000,0000,0000,,here, okay. Alright, so let's bury the\Nnoise. And to bury it in noise is, is
Dialogue: 0,0:02:23.06,0:02:28.50,Default,,0000,0000,0000,,amazingly eas y to do, right? So you have\Nyour function, and there it is, and all
Dialogue: 0,0:02:28.50,0:02:35.79,Default,,0000,0000,0000,,you got to do bury it in noise is, for\Nevery frequency component you got. Let me
Dialogue: 0,0:02:35.79,0:02:44.92,Default,,0000,0000,0000,,see where this ends. Here, so I'm FFT'ing\Nthe signal right? And all I gotta do is
Dialogue: 0,0:02:44.92,0:02:55.20,Default,,0000,0000,0000,,add, plus noise, times rand N um., this is\None by N, plus I times rand N, one by N.
Dialogue: 0,0:02:56.74,0:03:02.84,Default,,0000,0000,0000,,That's it, so like we did before except I\Nhaven't told you what noise is. So let's
Dialogue: 0,0:03:02.84,0:03:07.32,Default,,0000,0000,0000,,just do noise is equal to like, twenty.\NI'll just put a bunch of noise on it and
Dialogue: 0,0:03:07.32,0:03:15.24,Default,,0000,0000,0000,,let's look at this thing. Whoa, tell me if\Nyou see anything in there okay now that
Dialogue: 0,0:03:15.24,0:03:20.10,Default,,0000,0000,0000,,really bug becomes a real shit alright\Nwhatever or shit test right. Roshard
Dialogue: 0,0:03:20.10,0:03:28.15,Default,,0000,0000,0000,,whatever guy you see in there? Keon do you\Nsee anything in there no nothing dog cat
Dialogue: 0,0:03:28.15,0:03:35.60,Default,,0000,0000,0000,,your house you grew up in no nothing\Ncarpet. Okay, anybody else, want to
Dialogue: 0,0:03:36.02,0:03:41.05,Default,,0000,0000,0000,,volunteer anything else, better than\Ncarpet, no, okay. All right, by the way,
Dialogue: 0,0:03:41.05,0:03:46.64,Default,,0000,0000,0000,,this is what you got, to work with, right?\NAnd here's what a my claim is, if I keep
Dialogue: 0,0:03:46.64,0:03:52.16,Default,,0000,0000,0000,,taking samples of this thing, in fact, I\Nhave this thing, I have 21 samples, right,
Dialogue: 0,0:03:52.16,0:03:57.68,Default,,0000,0000,0000,,I haven't made any use of that fact.\NRight, I've 21 samples, these are all
Dialogue: 0,0:03:57.68,0:04:04.17,Default,,0000,0000,0000,,white noise, and in there is just this\Nclear line, that you cannot see. There is
Dialogue: 0,0:04:04.17,0:04:11.17,Default,,0000,0000,0000,,a signal sitting there, waiting for you to\Ngo get it. Okay, now lets talk about, if
Dialogue: 0,0:04:11.17,0:04:16.87,Default,,0000,0000,0000,,you have this, what does this do to here?\NSo that's what it looks like here what
Dialogue: 0,0:04:16.87,0:04:24.10,Default,,0000,0000,0000,,does it look like in the time domain. And\Nnot so hard to do you gotta inverse before
Dialogue: 0,0:04:24.10,0:04:31.87,Default,,0000,0000,0000,,you transform everything else you call\Nthat UN. all I gotta do I've gotta
Dialogue: 0,0:04:31.87,0:04:38.22,Default,,0000,0000,0000,,interverse 4A transform it. So I have to\Ngo, basically, now if you shoot. I FFT
Dialogue: 0,0:04:38.22,0:04:44.49,Default,,0000,0000,0000,,shifted it all ahead of time right into\Nthe absolute value. So, let's go and do
Dialogue: 0,0:04:44.49,0:04:51.52,Default,,0000,0000,0000,,some of that. Let's take out the absolute\Nvalue. Let's take off that FFT shift.
Dialogue: 0,0:04:52.66,0:04:59.38,Default,,0000,0000,0000,,Okay, all that hard work thrown away, fine\Nwe'll, we'll, we'll FFT shift it later.
Dialogue: 0,0:04:59.38,0:05:06.36,Default,,0000,0000,0000,,All we have to do is take the absolute\Nvalue here and FFT shift it there instead.
Dialogue: 0,0:05:06.66,0:05:22.84,Default,,0000,0000,0000,,Okay, but U of N now is just the IFFT of\NU, J. Okay, O UT sorry yeah. So I take row
Dialogue: 0,0:05:22.84,0:05:33.44,Default,,0000,0000,0000,,by row this noisy signal. I inversef ully\Ntransform it, and now I can say supply 211
Dialogue: 0,0:05:33.44,0:05:50.50,Default,,0000,0000,0000,,and we can just plot water fall TS\Nabsolute value of U and, Oh I need my view
Dialogue: 0,0:05:50.50,0:06:01.82,Default,,0000,0000,0000,,back. Okay, so here this is your problem.\NTell me if there's anything there. So
Dialogue: 0,0:06:01.82,0:06:06.62,Default,,0000,0000,0000,,remember data analysis is about this. So\Nwhat, what I like about these examples is
Dialogue: 0,0:06:06.62,0:06:11.31,Default,,0000,0000,0000,,in your dog problem or in this here. You\Nclearly saw, we already know the answer
Dialogue: 0,0:06:11.31,0:06:15.76,Default,,0000,0000,0000,,ahead of time. Right? We know there's a\Nsignal in there. We know there's this
Dialogue: 0,0:06:15.76,0:06:22.29,Default,,0000,0000,0000,,thing going like this through here. You\Ncan't see it cause I hit it, right? And
Dialogue: 0,0:06:22.29,0:06:27.21,Default,,0000,0000,0000,,the objective, if you are the airplane is\Nto hide yourself. The objective if you are
Dialogue: 0,0:06:27.21,0:06:32.01,Default,,0000,0000,0000,,there in that radar is to, is, is hide and\Ngo seek, right, and but it's, it's whoever
Dialogue: 0,0:06:32.01,0:06:36.81,Default,,0000,0000,0000,,has got the better, better data analysis\Nprocessing skills, right? There are things
Dialogue: 0,0:06:36.81,0:06:41.68,Default,,0000,0000,0000,,here you have to take advantage of. If you\Ndon't take advantage of them, you get no
Dialogue: 0,0:06:41.68,0:06:45.94,Default,,0000,0000,0000,,information, okay? And what's the\Ninformation you could take advantage of?
Dialogue: 0,0:06:45.94,0:06:51.72,Default,,0000,0000,0000,,So first of all in this problem. You may\Nnot even know where a filter exist put.
Dialogue: 0,0:06:51.72,0:06:57.09,Default,,0000,0000,0000,,What happens if this airplane bounces off\Nyour omeganaut? Suppose, okay? Let, let,
Dialogue: 0,0:06:57.09,0:07:02.46,Default,,0000,0000,0000,,let's play a what if game. Suppose you\Ndevelop really great stealth technology.
Dialogue: 0,0:07:02.46,0:07:07.90,Default,,0000,0000,0000,,This plane here you know how to put a, a\Nnice coating around your, your airplane.
Dialogue: 0,0:07:07.90,0:07:14.37,Default,,0000,0000,0000,,Design it so that you send omeganaut out.\NNothing comes back. Now, if you're these
Dialogue: 0,0:07:14.37,0:07:19.84,Default,,0000,0000,0000,,guys, you're like, wow, that's plane\Nvisible to me. However what if you're
Dialogue: 0,0:07:19.84,0:07:24.45,Default,,0000,0000,0000,,emitting some other frequency? There's\Nsomething else coming off your plane off
Dialogue: 0,0:07:24.45,0:07:28.94,Default,,0000,0000,0000,,the engine it wasn't something I shot out,\Nshot out there, but I have this big
Dialogue: 0,0:07:28.94,0:07:33.25,Default,,0000,0000,0000,,spectrum of stuff that I'm reading in.\NMaybe you're emitting at some other
Dialogue: 0,0:07:33.25,0:07:38.57,Default,,0000,0000,0000,,frequency some information that I could\Nget. I don't even know what frequency I
Dialogue: 0,0:07:38.57,0:07:43.84,Default,,0000,0000,0000,,should be lookin for. But if I keep taking\Nmeasurements what this is going to allow
Dialogue: 0,0:07:43.84,0:07:48.91,Default,,0000,0000,0000,,me to do is come back to this idea here,\Nis to say, here's what I'm picking up
Dialogue: 0,0:07:48.91,0:07:53.99,Default,,0000,0000,0000,,which just looks like nothing. And what I\Nwant to start doin, slice by slice, is I
Dialogue: 0,0:07:53.99,0:07:59.26,Default,,0000,0000,0000,,just keep taking information in, start\Naveraging it. Because anything that's real
Dialogue: 0,0:07:59.26,0:08:04.40,Default,,0000,0000,0000,,signal is not going to cancel out. Noise\Nshould cancel out, right? So then if I get
Dialogue: 0,0:08:04.40,0:08:12.58,Default,,0000,0000,0000,,all the noise cancellation happening.\NOkay, sorry for the pause. Alright, ready?
Dialogue: 0,0:08:12.58,0:08:17.91,Default,,0000,0000,0000,,So if I get all the noise cancelling out,\NI will start to see emerging out of this
Dialogue: 0,0:08:17.91,0:08:23.11,Default,,0000,0000,0000,,frequency component a signature there,\Nsomewhere. And maybe I don't know where it
Dialogue: 0,0:08:23.11,0:08:27.86,Default,,0000,0000,0000,,is ahead of time, and if I see it. Then\Nyou can say well, you didn't put a filter
Dialogue: 0,0:08:27.86,0:08:31.77,Default,,0000,0000,0000,,around here, get rid of everything else\Nput the filter there, see what it says
Dialogue: 0,0:08:31.77,0:08:35.69,Default,,0000,0000,0000,,over here. See if there's a signal there,\Nright. So this is the kind of stuff you
Dialogue: 0,0:08:35.69,0:08:39.65,Default,,0000,0000,0000,,would want to do. It's all about who's\Nbetter at signal processing actually, at
Dialogue: 0,0:08:39.65,0:08:43.61,Default,,0000,0000,0000,,the end of the day. Alright, so I've given\Nyou this example here which is, sort of
Dialogue: 0,0:08:44.04,0:08:49.73,Default,,0000,0000,0000,,just using very basic time frequency.\NWhich is I can represent the whole signal
Dialogue: 0,0:08:49.73,0:08:54.92,Default,,0000,0000,0000,,in time or I can represent it in\Nfrequency. Now what we're going to move
Dialogue: 0,0:08:54.92,0:09:00.97,Default,,0000,0000,0000,,onto is much more sophisticated thinking.\NWhich is to say, wait a minute, somehow.
Dialogue: 0,0:09:00.97,0:09:05.25,Default,,0000,0000,0000,,When I go from time to frequency, if I'm\Nin the frequency domain, it tells me
Dialogue: 0,0:09:05.25,0:09:09.87,Default,,0000,0000,0000,,nothing about the time domain. If I'm in\Nthe time domain, it tells me nothing about
Dialogue: 0,0:09:09.87,0:09:13.98,Default,,0000,0000,0000,,frequency. I want both pieces of\Ninformation at the same time. And this is
Dialogue: 0,0:09:13.98,0:09:18.37,Default,,0000,0000,0000,,where time/frequency analysis comes in\Nwhich is to say, I would trade a little
Dialogue: 0,0:09:18.37,0:09:22.88,Default,,0000,0000,0000,,bit of what I know in the time domain for\Na little information on the frequency
Dialogue: 0,0:09:22.88,0:09:26.59,Default,,0000,0000,0000,,domain. I'm not going to give up\Neverything I know in the time domain.
Dialogue: 0,0:09:26.59,0:09:30.93,Default,,0000,0000,0000,,They're not separate objects. They, I'm\Ngoing to use both at the same time, okay?
Dialogue: 0,0:09:30.93,0:09:35.28,Default,,0000,0000,0000,,Remember you can not know everything about\Ntime and frequency at the same time.
Dialogue: 0,0:09:35.70,0:09:40.10,Default,,0000,0000,0000,,Impossible, through the idea of the\NFourier transform, the idea of Heisenberg
Dialogue: 0,0:09:40.10,0:09:44.68,Default,,0000,0000,0000,,uncertainty. That's not a possibility for\Nyou. However, you can sacrifice one for
Dialogue: 0,0:09:44.68,0:09:49.31,Default,,0000,0000,0000,,the other to try to get yourself in a\Nsituation where you can know a little bit
Dialogue: 0,0:09:49.31,0:09:53.100,Default,,0000,0000,0000,,about both and maybe make some information\Nthere. Okay? Alright, so Wednesday, we're
Dialogue: 0,0:09:53.100,0:09:58.46,Default,,0000,0000,0000,,going to talk about window Fourier\Ntransforms, which is this idea of how do I
Dialogue: 0,0:09:58.46,0:10:02.91,Default,,0000,0000,0000,,represent both. In the meantime, you have\Nyour dog problem, and we'll just keep
Dialogue: 0,0:10:02.91,0:10:04.42,Default,,0000,0000,0000,,moving forward from there.